This is a beautiful puzzle that came to me through an IITD friend (Sirisha), and I had not done before – thank you Sirisha!
There are two friends A and B. Their teacher calls them separately and tells A, the sum of two numbers (both between 0 and 9, repetition allowed) and tells B, the product of both numbers
A and B then talk. A says – I dont know the two numbers. B says – Even I dont. A says – Now I do. B says – even I do now
Both A and B are good at mathematics.
What are the two numbers?
As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.
Happy number hunting!
Alok Goyal's Puzzles Page 
The answer is 2 and 3.
Had to take help of excel for killing options here ..
Vishal
Gupta
Thanks Vishal, there must have been some mistake, the correct answer is 2 and 2. Sorry did not get a chance to respond for so long!